On the Existence and Uniqueness Results for Fuzzy Linear and Semilinear Fractional Evolution Equations Involving Caputo Fractional Derivative by Ali El Mfadel, Said Melliani, M’hamed Elomari

“…The existence theorems are proved by using fuzzy fractional calculus, Picard’s iteration method, and Banach contraction principle. …”
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Signal Processing for Nondifferentiable Data Defined on Cantor Sets: A Local Fractional Fourier Series Approach by Zhi-Yong Chen, Carlo Cattani, Wei-Ping Zhong

“…Our results can be observed as significant extensions of the previously known results for the Fourier series in the framework of the local fractional calculus. Some examples are given to illustrate the efficiency and implementation of the present method.…”
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Warehouse mobile access network security associate pre-anticipated notification scheme based on AAA authentication by Yong-hui ZHANG, Zhang-xi LIN, Jian-hua LIU, Quan LIANG

“…A security pre-anticipated notification scheme was proposed for network mobility,based on AAA authentication.Pre-judged handover by wireless sensor network locating,security association information context was triggered to forward to data processing center in corresponding node router,in order to achieve trust authentication in advance.The scheme models on Pi calculus proved its compatibility with NEMO basic protocol.Analysis results display that costs become the half and simulations results show delay and resource occupied reduces significantly.…”
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Almost Periodic Functions on Time Scales and Applications by Yongkun Li, Chao Wang

“…We first propose the concept of almost periodic time scales and then give the definition of almost periodic functions on almost periodic time scales, then by using the theory of calculus on time scales and some mathematical methods, some basic results about almost periodic differential equations on almost periodic time scales are established. …”
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Degenerate r-Bell Polynomials Arising from Degenerate Normal Ordering by Taekyun Kim, Dae San Kim, Hye Kyung Kim

“…Recently, Kim-Kim introduced the degenerate r-Bell polynomials and investigated some results which are derived from umbral calculus. The aim of this paper is to study some properties of the degenerate r-Bell polynomials and numbers via boson operators. …”
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Robot-Assisted Removal of a Partially Intravesical Intrauterine Device (IUD) and Large Bladder Stone by Cassandra Heaney, Paul Lee, Andrew Winer

“…We present a case report of a 41-year-old woman who was found to have a partially intravesical IUD and associated 2.4 cm bladder calculus. Removal of the intravesical IUD and stone was achieved with cystoscopy, cystolitholapaxy, and robot-assisted laparoscopic cystotomy.…”
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Oscillation of Nonlinear Fractional Dynamic Equations with Forcing Term by S. Manikandan, V. Muthulakshmi, S. Harikrishnan, Porpattama Hammachukiattikul

“…Our approach is determined from the implementation of generalized Riccati transformation, some properties of conformable time-scale fractional calculus, and certain mathematical inequalities. Also, we extend the study of oscillation to conformable fractional Euler-type dynamic equation. …”
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On the finite Fourier transforms of functions with infinite discontinuities by Branko Saric

“…The introductory part of the paper is provided to give a brief review of the stability theory of a matrix pencil for discrete linear time-invariant singular control systems, based on the causal relationship between Jordan's theorem from the theory of Fourier series and Laurent's theorem from the calculus of residues. The main part is concerned with the theory of the integral transforms, which has proved to be a powerful tool in the control systems theory. …”
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Fractional Order Models of Industrial Pneumatic Controllers by Abolhassan Razminia, Dumitru Baleanu

“…In the light of fractional calculus, a fractional order derivative-derivative (FrDD) controller and integral-derivative (FrID) are remodeled. …”
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Local Fractional Fourier Series with Application to Wave Equation in Fractal Vibrating String by Ming-Sheng Hu, Ravi P. Agarwal, Xiao-Jun Yang

“…We introduce the wave equation in fractal vibrating string in the framework of the local fractional calculus. Our particular attention is devoted to the technique of the local fractional Fourier series for processing these local fractional differential operators in a way accessible to applied scientists. …”
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Multivariate Dynamic Sneak-Out Inequalities on Time Scales by Ammara Nosheen, Aneeqa Aslam, Khuram Ali Khan, Khalid Mahmood Awan, Hamid Reza Moradi

“…In seeking applications, these inequalities are discussed in classical, discrete, and quantum calculus.…”
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The Use of Cubic Splines in the Numerical Solution of Fractional Differential Equations by W. K. Zahra, S. M. Elkholy

“…Fractional calculus became a vital tool in describing many phenomena appeared in physics, chemistry as well as engineering fields. …”
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Adaptive Fractional Fuzzy Sliding Mode Control for Multivariable Nonlinear Systems by Junhai Luo, Heng Liu

“…The fractional order calculus is employed in the parameter updating stage. …”
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Efficient Variational Approaches for Deformable Registration of Images by Mehmet Ali Akinlar, Muhammet Kurulay, Aydin Secer, Mustafa Bayram

“…Image registration, an ill-posed optimization problem, is solved using a gradient-descent-based method and some fundamental theorems in calculus of variations. Euler-Lagrange equations with homogeneous Neumann boundary conditions are obtained. …”
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Compensating Trajectory of a Kind of Long-pitch Constrained Conveyor Chain by Li Shujing, Hong Lin, Liang Yanshu

“…The conveyor chain model which include constrained and free pin is established.Through analyzing each position of pin in static and the movement velocity and displacement of pin in one period are calculated according to its coordinate.The mathematical model of each pin in the state of motion is established and the motion trajectory of free pin should include two parts because of the polygonal action of the chain is proposed.Aiming at the problem of the nonlinear equations in the mathematical model of chain is hard to calculate,a kind of solution method based on fundamental theorem of calculus is presented.Finally,motion trajectory of top and bottom edge free pin is obtained by using the MATLAB point depiction method.A computation method is provided for the analysis of trajectory constrained conveyor chain and the design of constrained trajectory.…”
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Option Pricing under the Subordinated Market Models by Longjin Lv, Changjuan Zheng, Luna Wang

“…Firstly, we prove that the subordinated Brownian motion controlled by the fractional diffusion equation has many financial properties, such as self-similarity, leptokurtic, and long memory, which indicate that the fractional calculus can describe the financial data well. Then, we investigate the option pricing under the assumption that the stock price is driven by the subordinated Brownian motion. …”
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Analytical Solutions of Fractional Differential Equations Using the Convenient Adomian Series by Xiang-Chao Shi, Lan-Lan Huang, Zhen-Guo Deng, Dan Liu

“…Due to the memory trait of the fractional calculus, numerical or analytical solution of higher order becomes very difficult even impossible to obtain in real engineering problems. …”
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Traumatic fibroma – a review by Marco Antonio Rocafuerte - Acurio

“…The traumatic fibroma is a reactive fibrous hyperplasia caused by trauma or local irritation, such as the presence of calculus, overhanging margins of restorations, orthodontic appliances, among others. …”
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Multipoint BVP for the Langevin Equation under φ-Hilfer Fractional Operator by Mohammed A. Almalahi, Satish K. Panchal, Fahd Jarad

“…At first, we derive the equivalent solution to the proposed problem at hand by relying on the results and properties of the generalized fractional calculus. Next, we investigate and develop sufficient conditions for the existence and uniqueness of solutions by means of semigroups of operator approach and the Krasnoselskii fixed point theorems as well as Banach contraction principle. …”
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ABC Fractional Derivative for Varicella-Zoster Virus Using Two-Scale Fractal Dimension Approach with Vaccination by Jirong Yang, Farkhanda Afzal, Perpetual Appiah

“…At the end, we provide the graphical results showing the effectiveness of two-scale dimension and fractional calculus in the current model.…”
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